Date: Apr 23, 2013 1:26 PM
Author: Waldek Hebisch
Subject: Re: An independent integration test suite

clicliclic@freenet.de wrote:
>
> Axel Vogt schrieb:

> >
> > ...

> > > ch. ex's Der. Fri. Mpl MMA etc. etc.
> > > 6.10 1.20 17 ...
> > > ----------------------------------------------
> > > 1 81 78 80 80 ??
> > > 2 90 - - - -
> > > 3 14 - - - -
> > > 4 132 - - - -
> > > 5 120 - - - -
> > > 6 26 - - - -
> > > 7 11 - - - -
> > > 8 59 - - - -
> > > --------------------------------------------
> > > 100% 96.3% 98.8% 98.8% ????%

> > ...
> >
> > Let's go to Chap 3, 6 and 7 ( in a new thread ) ?

>
> Yes, same thread or different thread, would make no difference to me. I
> am working on Ch. 4, as I said, but in a _very_ relaxed way.
>
> It has occured to me that Waldek should post the FriCAS results for the
> two cases he could not verify by differentiation. Perhaps they are
> correct, perhaps not. I doubt that results with mixed branches should be
> counted as successes: numerical evaluation would fail even on FriCAS, I
> suppose.
>


(1) -> integrate((asin(x/a)*asin(x/a)^(1/2))/((-1*x^2+a^2)^(1/2)), x)

+-------------------+
x 2 | x
2atan(------------) |2atan(------------)
+---------+ | +---------+
| 2 2 | | 2 2
\|- x + a \| \|- x + a
(1) ------------------------------------------
+-+
5\|2
Type: Union(Expression(Integer),...)
(2) -> integrate(acos((x/(x+1))^(1/2)), x)

+-----+
1 | x +-----+
(2) (x + 1)atan(----------------) + |----- \|x + 1
+-----+ \|x + 1
| x +-----+
|----- \|x + 1
\|x + 1
Type: Union(Expression(Integer),...)


--
Waldek Hebisch
hebisch@math.uni.wroc.pl